Your main problem will be insufficient tank space. A 10g well-planted could house a pair [make sure it is a true male/female pair] of Mikrogeophagus ramirezi [I'm assuming it is the common or blue ram you refer to, since this one needs the warmth unlike the Bolivian Ram] but managing two groups of shoaling fish as well is pushing the limits.
One must remember than all of the characins and cyprinids (tetras, hatchets, rasbora, barbs) are shoaling fish that require a group of 6 or more, five in a pinch. And most of these attain sizes that would be very limiting for a 10g. The barbs are definitely out, there is no species small enough to manage in a group of 5 in a 10g, they are active swimmers that need length just for that.
Having said that, there are some lovely dwarf characins (Ember Tetra) and rasbora (the Boraras species) that would work though. Of these I would suggest the Boraras rasbora species which tend to remain in the top half of the tank and would contrast well with the rams that tend to remain in the lower third. Boraras need floating plants, and this would also help the rams who will appreciate the "cover" and be more out and about as a result. The Boraras species are very small, I have 9 of Boraras brigittae in a 10g and can hardly see them
. You can read about these in our profiles, just click on any of the shaded names to go to that species' profile.